Is the ZLB an economic or legal constraint?

The so-called zero-lower-bound (ZLB) plays a prominent role in modern (and even older) macroeconomic theories. It is often introduced in a paper or at conference as a fact of life -- an unavoidable property of the physical environment, like gravity. But is it correct to view it in this way? Or is the ZLB better thought of as legal constraint--something that can potentially be circumvented by policy?

The Financial Services Regulatory Relief Act of 2006 allows the U.S. Federal Reserve (the Fed) to pay interest on reserve accounts that private banks hold at the Fed. Specifically, the Act states that:

Balances maintained at a Federal Reserve bank by or on behalf of a depository institution may receive earnings to be paid by the Federal Reserve bank at least once each calendar quarter, at a rate or rates not to exceed the general level of short-term interest rates.

The effective date of this authority was advanced to October 1, 2008, by the Emergency Economic Stabilization Act of 2008.

It is not clear (to me, at least) whether the Act grants the Fed the authority to pay a negative interest rate on reserves. Note that if the interest-on-reserves (IOR) rate is set to a negative number, then banks would in effect be paying the Fed a "service fee" for the privilege of holding reserve balances with the Fed. But if the Fed is not legally permitted to use negative interest rate policy (NIRP), then the ZLB is obviously a legal constraint.

This legal constraint, however, may not be binding if the ZLB is also an economic constraint. In fact, the traditional explanation for the ZLB is the existence of physical currency bearing zero interest. The idea that arbitrage will effectively keep interest rates from falling below zero is deeply ingrained in the minds of economists. For example, Corriea, et. al. (2012) write:

Arbitrage between money and bonds requires nominal interest to be positive. This "zero bound" constraint gives rise to a macroeconomic situation known as a liquidity trap. It presents a difficult challenge for stabilization policy.

However, we know from recent experience that the ZLB appears not to be an economic constraint.  Several central banks today have set their deposit rates into negative territory:

There is currently over $10 trillion of government debt in the world yielding a negative nominal interest rate; see here. As of this writing, even long bonds like the German 10-year Bund are in negative territory.

Well, alright, so the ZLB is evidently not an economic constraint. But surely there is some limit to how low nominal interest rates can fall? This lower limit is called the effective lower bound (ELB). And economic theory is clear: if we're at the ELB in a recession, then monetary policy has done about as much as it can be expected to do.

But what exactly is the ELB? Is it -1%, -2%, -5%, or perhaps even lower? Economists like Miles Kimball believe it to sufficiently negative to warrant NIRP as an effective policy tool; see here (see also the discussion by Ken Rogoff in chapter 10 of his book). These arguments, however, did not seem to gain much traction. For example, in the present discussions concerning the Fed's new long-run monetary policy framework, the possibility of NIRP is not even mentioned. But perhaps it should be if the ELB is in fact significantly below zero. In what follows, I want to make my own (related) argument for why the ELB is probably a lot lower than most people think.

Suppose the Fed was to set the IOR to -10% (in a deep demand-driven recession, this would presumably be accompanied with a promise to raise the IOR at some point in the future). The traditional economic argument suggests that any security dominated in rate of return by cash would in this case be driven out of circulation.

The first thing we could imagine happening is banks attempting to convert their digital reserves into vault cash. Banks are presently holding over $1.6 trillion in reserves with the Fed. The largest denomination Federal Reserve note is $100. This is what $1 trillion in $100 bills apparently looks like:

That's about the size of a football field. Banks would not convert all of their reserves into cash--even if it was costless to do so--because they'd need about $20-30 billion or so to make interbank payments. Of course, managing all that cash would be far from costless. But there is a simpler reason for why banks would not make the conversion. The Fed could simply charge banks a 10% service fee on their vault cash.

Alright, well what effect is the -10% IOR rate going to have on the deposit rate (or fees) that banks offer (or charge) their depositors? Banks are not likely to pass the full cost on to their depositors, especially if they view the NIRP to be temporary, because they'll want to maintain their customer relationships.

But let us take the extreme case and suppose that NIRP is perceived to be permanent. Then surely deposit rates will decline (or bank fees will rise) significantly. Deposit rates may even decline to the point where depositors start withdrawing their money from the banking system. Banks may well let this source of funding go if they could borrow more cheaply from the Fed (banks would need to borrow reserves to honor the withdrawal requests of their customers). Of course, the Fed lending rate is also a policy variable and could, in principle, be lowered to negative territory as well.

But how realistic is it to imagine all or most bank deposits converted to cash? While this might be the case for small value accounts, it seems unlikely that the business sector would be able to manage its payments needs without the aid of the banking system. Even money market funds need to work through the banking system. I suppose one could imagine a new product created by (say) Vanguard in which they create a cash fund with equity shares redeemable for cash that is collected and stored in rented Las Vegas vault. But the moment the activity is intermediated, it becomes taxable. If the Fed is not permitted to tax (oops, charge a service fee) such entities, the fiscal authority could, in principle, implement a surcharge that is set automatically off the IOR rate in some manner.

I think in this way one can see how the ELB might easily be well below -5% (or more). This is probably low enough to allow us to disregard the ELB as a binding economic constraint. The relevant constraint is always a legal one. And laws can be changed if it is deemed to serve the public interest.

Keep in mind that in a large class of economic models, ranging from Keynes (1936) to New Keynesian, there is potentially much to be gained by eliminating the ZLB. If these models are wrong, then let's get rid of them. But if they're roughly correct, why don't we take their policy prescriptions seriously? Let's stop talking about the ZLB as if it's a force of nature. It is a policy choice. And if it's a bad policy choice, it should be changed.

The Chicago Booth Survey on MMT

I want to say a few things about Chicago Booth's recent survey questions posed to a set of economists; see here. The survey asked how strongly one believes in the following two statements:

Question A: Countries that borrow in their own currency should not worry about government deficits because they can always create money to finance their debt.

Question B: Countries that borrow in their own currency can finance as much real government spending as they want by creating money.

Not surprisingly, most economists surveyed disagreed with both statements. Fine. But, not fine, actually. Because the survey prefaced the two questions with 

Modern Monetary Theory

as if the the two statements constitute some core belief of MMT.  

Was any MMT proponent included in the survey? Don't be ridiculous, of course not (there were a couple from MIT though--perhaps they thought this was close enough). How would a typical MMT proponent have answered these two questions? I am sure that most would have answered in the exact same way as other economists. If this is the case, then why does Chicago Booth preface the survey with MMT? There are many possibilities, none of which are attractive for Chicago Booth.

Let's consider Question B first. Or, better yet, let's not. This question is so ridiculous it hardly merits a response. Nobody believes that governments face no resource constraints.

O.K., so let's consider Question A, where some legitimate confusion may be present. Before I start though, I want to make clear that I don't purport to know the entire MMT academic literature very well. But I have done some reading and I have corresponded with some very smart, very thoughtful MMT proponents. I don't agree with many of their views, but I think I see how some of what they say is both valid and contrary to conventional thinking. At the very least, it seems worth exploring. What I am about to say is my own interpretation -- I am not speaking on behalf of MMTers.

Alright, so on to the question of whether deficits "matter." The more precise MMT statement reads more like this "A country that issues debt denominated in its own currency operating in a flexible exchange rate regime need not worry about defaulting in technical terms on its outstanding debt." That is, the U.S. government can always print money to pay for its maturing debt. That's because U.S. Treasury securities represent claims for U.S. dollars, and the government can (if it wants) print all the dollars it needs. 

Nobody disagrees with this statement. MMTers like to make it explicit because, first, much of the general public does not understand this basic fact, and second, this misunderstanding is sometimes (perhaps often) used to promote particular ideological views on the "proper" role of government.

Mainstream economists, like myself, like to point out what matters is not technical default but economic "default." An unexpected inflation whittles away the purchasing power of those caught holding old money as new money is printed to pay for whatever. I think it's clear that MMTers understand this too. This can be seen in their constant reference to an "inflation constraint" as defining the economic limits to government spending. I tried to formalize this idea in my previous blog post; see here: Sustainable Deficits.

But it's more complicated than this -- and in interesting ways, I think. Consider a large corporation, like General Motors. GM issues both debt and equity. The debt GM issues is denominated in dollars, so it can go bankrupt. But GM also issues a form of "money"--that is, is can use newly created equity to pay its employees or to make acquisitions.

Issuing more equity does not expose GM to greater default risk. Indeed, it may very well reduce it if the equity is used to buy back GM debt. If GM is thinking about financing an acquisition through new equity issuance, the discussion is not going to about whether GM can afford to print the new shares. Of course it can print all the shares it wants. The question is whether the acquisition is accretive or dilutive. If the former, then issuing new money will make the value of GM money go up. If the latter, then the new share issue will be inflationary (the purchasing power of GM shares will go down). In other words, "deficits don't matter" in the sense that the outstanding GM liabilities do not matter per se -- what matters is something more fundamental. Equity "over-issue" may not be desirable, but the phenomenon is symptomatic, not causal.

The U.S. government and Federal Reserve in effect issue equity. The government need not default on its debt. This is because U.S. Treasury debt is convertible into money (equity) and the Fed can do so if it so chooses. The question for the government, as with GM, is whether any new spending program is accretive or dilutive. If the economy is operating at less than full capacity, then this is like GM being presented with a positive NPV investment opportunity. The government can issue new money that, if used wisely, need not be inflationary.

There are limits to how far this can go, of course. And there was the all important qualifier "if used wisely." But this is exactly where the debate should be: how should our institutions be designed to promote the "best" allocation of resources?

I often hear that MMTers don't have a good theory of inflation. As if there is a good theory of inflation out there already. But I see in MMT a theory of inflation that overlaps (not entirely) with my own views expressed, say, here: The Failure to Inflate Japan. The MMT view seems to take a broader view over the set of instruments that monetary policy may employ to control inflation. We can have a debate about the merits of their views, but there's no reason to dismiss them outright or to pretend they don't have a theory of inflation.

Another complaint I hear: the MMTers don't want to produce a model. You know, it's true, there are not many mathematical models out there. So what? 

First, the lingua franca of policy making is English -- math is a part of a trade language. Economic ideas can be understood when expressed in the vernacular. It's also been helpful to me and others to attempt to "formalize" our thoughts in our trade language. But it seems to me that some of my colleagues can only understand an argument if it's posed in their trade language. This is a rather sad state of affairs, if true. 

Second, MMT, like any school of thought, is evolving over time and comes from a different tradition. Instead of demanding a model (now!), why not reach out and try to help formalize some of their ideas. You never know -- you may actually learn something in the process.

I could go on, but will stop here for now. 

Sustainable deficits

There's been much welcome discussion of late concerning the sustainability of government budget deficits and whether the size of the public debt is anything to worry about. I'm not going to answer this question for you here today. But what I would like to do is describe a framework that economists frequently employ to help organize their thinking on the matter. I want to begin with some simple arithmetic and then move on to a bit of theory. I'll let you judge whether the framework has any merit.

Let's start with some standard definitions.
G(t) = government spending (purchases and transfers) in year t.
T(t) = government tax revenue in year t.
R(t) = gross nominal interest rate on government debt paid in year t+1.
D(t) = nominal government debt in year t (including interest-bearing central bank reserves).

Now let's link these objects together using the following identity:

[1] G(t) + [R(t-1) - 1]*D(t-1) = T(t) + [D(t) - D(t-1)]

In words, the left-hand-side (LHS) of the identity measures the money needed to pay for government spending G(t) and the interest expense of the debt [R(t-1) - 1]*D(t-1), where [R(t-1) - 1] denotes the net nominal interest rate. The right-hand-side (RHS) of the identity measures the money collected by the government in the form of taxes T(t) and the money created through new nominal debt issuance [D(t) - D(t-1)].

I find it convenient to rewrite [1] as,

[2] G(t) - T(t) = D(t) - R(t-1)*D(t-1)

The LHS of [2] represents the primary government budget deficit. If the deficit is positive in period t, then the RHS of [2] tells us that the stock of debt in period t must be larger than the interest plus principal of the debt maturing from period t-1.

Next, define n(t) = D(t)/D(t-1), that is, the (gross) rate of growth of the nominal debt. Use this definition to write D(t-1) = D(t)/n(t) and substitute this expression into [2] to form,

[3] G(t) - T(t) = [1 - R(t-1)/n(t)]*D(t)

Let Y(t) denote the nominal GDP. Now define g(t) = G(t)/Y(t), τ(t)=T(t)/Y(t) and d(t) = D(t)/Y(t). Because I want to limit attention to "long run" scenarios, let me impose a stationarity restriction: g(t) = g, τ(t) = τ, d(t) = d, R(t-1) = R, and n(t) = n. Then we can write [3] as,

[4] g - τ = [1 - R/n]*d

Assuming d > 0, the identity [4] tells us that a sustained primary deficit is possible only if R < n. Recall that R represents the (gross) nominal interest rate on government debt and n represents the (gross) rate of growth of the nominal debt. Because of my stationarity assumption d = D(t)/Y(t), it follows that n also represents the (gross) rate of growth of the nominal GDP.

A lot of mainstream thinking on the matter of "fiscal sustainability" is rooted, I think, in the assumption that R > n. In the standard DSGE model (which abstracts from financial market frictions), the "real" interest rate R/n is pinned down by time-preference and productivity growth. This real interest rate is typically estimated to be a positive number. If this is the view one adopts, then condition [4] implies that budget deficits cannot be sustained into the indefinite future. It's not exactly made clear what might happen if deficit finance persists in such a case -- maybe inflation and/or default. Bond vigilantes. Something like that.

But this view is, at best, seriously flawed. First of all, as just an empirical matter, R < n seems like a better approximation than R > n. Here the year-over-year growth rate of nominal GDP and the one-year Treasury-bill rate for the U.S. economy since 1961,

Secondly, the standard DSGE model ignores the role that U.S. Treasury debt plays as an exchange medium in financial markets. The growth in the demand for Treasury debt has come from many sources over the past few decades. It is used extensively as collateral in credit-derivative and repo markets. Foreign countries have clamored to accumulate U.S. Treasuries as a store of value. Its demand was further enhance as a "flight to safety" asset during the financial crisis. And more recently, changes in financial regulations (Dodd-Frank and Basel III) have further spurred the demand for Treasuries (for example, they can be used to satisfy the Basel III liquidity-coverage-ratio requirement for banks).

Because of the special role played by nominally safe government debt in financial markets, it can trade at a premium. That is, agents and agencies are willing to hold "monetary" objects for reasons other than their pecuniary rate of return. This is why the nominal (and real) interest rate on safe government securities can be set lower than the "natural" rate of interest. If R < n, then the RHS of [4] corresponds to seigniorage revenue. (Note: seigniorage is not limited to the purchasing power created by zero-interest cash.)

Some of this discussion seems related to what the MMT folks are talking about. I'm not an expert in that area (am still reading up on it), but see, for example, Scott Fullwiler's article: The Debt Ratio and Sustainable Macroeconomic Policy. There's also this nice piece by (the more mainstream) Neil Mehrotra: Debt Sustainability in a Low Interest Rate World and, of course, Olivier Blanchard's AEA Presidential Address: Public Debt and Low Interest Rates.

Are there limits to how large a sustainable deficit might be? To answer this question, we need to go beyond the identities described above. Here's a simple theoretical restriction: Assume that the demand for real debt d is increasing in its real yield R/n. In undergraduate money-macro textbooks, we might say "assume that the demand for money is increasing in the interest rate paid on money." Note that for a given nominal interest rate R, this implies that the demand for real money balances is decreasing in the (expected) inflation rate. Let's denote this theory of money demand by the behavioral equation:

[5] d = L(R/n), with L increasing in R/n.

Combine the theoretical statement [5] with the identity in [4] to form a government budget constraint:

[6] g - τ = [1 - R/n]*L(R/n)

Now, to discover the limit of how large the deficit can get, imagine that the government wants to maximize the sustainable deficit through its choice of R/n (all that matters here is the ratio). What are the limits to seigniorage revenue?

The answer to this question has a standard "Laffer curve" property to it. Increasing R (or decreasing n) is bad because doing so increases the interest expense of the debt. On the other hand, it increases the demand for debt. Think of [1 - R/n] as the tax rate and L(R/n) as the tax base. Increasing R/n has competing effects. So, for example, increasing n has the effect of increasing the inflation tax rate. This is good for revenue purposes. But it also has the effect of decreasing the tax base (as people substitute out of government debt into competing securities). This is bad for revenue purposes. The revenue (primary deficit) maximizing interest/inflation rate equates these two margins. In short, economic behavior places a restriction on how much the government can finance its operations through money/debt issuance.

This is a very simple theory and it can be extended in many different and interesting ways. But the point of this blog post was first, to demonstrate how government budget identities can be combined with economic theory to form a meaningful government budget constraint and second, to demonstrate that there's nothing necessarily wrong or unsustainable about a government running a persistent budget deficit.


Postscript: March 12, 2019

I should have figured that Nick Rowe beat me to this post; see here. He also provides this nice Laffer curve diagram.

In the diagram above, r corresponds to my R and g corresponds to my n. I think I would have drawn the diagram with seigniorage revenue on the y-axis and the real interest rate (R/n) on the x-axis. Then (R/n)* would denote the seigniorage revenue maximizing real yield on government debt.

Nick points out that in the OLG model, the introduction of (say) land eliminates the possibility that R < n in equiilbrium. This is true only if government debt serves only as a store of value. My paper with Fernando Martin uses a standard macro model where debt has a liquidity role and coexists with a higher yielding alternative asset. It also has a diagram like Nick's (Figure 1).

A final thought. One often hears MMTers say something like "we replace the government budget constraint with an inflation constraint." I interpret this statement in the following way. Imagine setting the nominal interest rate to its lower bound R = 1 (I actually think it can go lower). Then the real rate of return on government debt (zero-interest money) is 1/n. If the real GDP is constant, then n represents the equilibrium inflation rate (in a model where we impose the additional market-clearing restriction). Assuming we are on the LHS of the Laffer curve, increasing the inflation rate increases the primary deficit. An inflation constraint n < n* then limits how large the primary deficit can be.